You've got an array, consisting of n integers: a1,a2,...,an. Your task is to quickly run the queries of two types: Assign value x to all elements from l to r inclusive. After such query the values of the elements of array al,al+1,...,ar become equal to x. Calculate and print sum , where k doesn't exceed 5. As the value of the sum can be rather large, you should print it modulo 1000000007(109+7).

Input The first line contains two integers n and m (1 \le n,m \le 105), showing, how many numbers are in the array and the number of queries, correspondingly. The second line contains n integers: a1,a2,...,an (0 \le ai \le 109) - the initial values of the array elements.Then m queries follow, one per line: The assign query has the following format: "", (1 \le l \le r \le n;0 \le x \le 109). The query to calculate the sum has the following format: "", (1 \le l \le r \le n;0 \le k \le 5). All numbers in the input are integers.

Output For each query to calculate the sum print an integer - the required sum modulo 1000000007(109+7).